Pressure temperature cross spectra are necessary in predicting noise propagation in regions of velocity gradients downstream of combustors if the effect of convective entropy disturbances is included. Pressure temperature cross spectra and coherences were measured at spatially separated points in a combustion rig fueled with hydrogen. Temperature-temperature and pressure-pressure cross spectra and coherences between the spatially separated points as well as temperature and pressure autospectra were measured. These test results were compared with previous results obtained in the same combustion rig using Jet A fuel in order to investigate their dependence on the type of combustion process. The phase relationships are not consistent with a simple source model that assumes that pressure and temperature are in phase at a point in the combustor and at all other points downstream are related to one another by only a time delay due to convection of temperature disturbances. Thus these test results indicate that a more complex model of the source is required.